Related papers: Linked cluster expansion of the many-body path int…
We present a novel analytical approach for the calculation of the mean density of states in many-body systems made of confined indistinguishable and non-interacting particles. Our method makes explicit the intrinsic geometry inherent in the…
Recent progress in the numerical solution of the nuclear many-body problem and in the development of nuclear Hamiltonians rooted in Quantum Chromodynamics, has opened the door to first-principle computations of nuclear reactions. In this…
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
An important quantity in liquid state theory is the radial distribution function $g(r)$. It can be calculated within the framework of classical density functional theory in two very distinct ways. In the test-particle route, one fixes a…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the cellular dynamical mean-field…
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster…
The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved…
We introduce a novel many body method which combines two powerful many body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method…
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
Lennard-Jones clusters, while an easy system, have a significant number of non equivalent configurations that increases rapidly with the number of atoms in the cluster. Here, we aim at determining the cluster partition function; we use the…
The density functional scheme for calculating the pair density is presented by means of the constrained-search technique. The resultant single-particle equation takes the form of the modified Hartree-Fock equation which contains the kinetic…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the…
Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through…
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…
We develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schr\"odinger equation are approximated by a hierarchy of polynomial systems at…
We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way…